Forgetting BIAB for a second, it's a better system if you are able to specify what you don't want. I agree one might not play a seventh in a ninth chord, but likewise one might leave out the fifth, or even the root if there is a bass. Leaving out the third is common too. When I write something like this, I actually write "No 3rd" or similar.

I won't venture into what might be convention anywhere else, but in American jazz, whatever extension you put on a triad is assumed to possibly include all extensions below it. 9th includes dominant 7; 11th includes dominant 7 & major 9; and 13th includes dominant 7, major 9 and often perfect 11.


BIAB 2025 Win Audiophile. Software: Studio One 7 Pro, Swam horns, Acoustica-7, Notion 6, Song Master Pro, Win 11 Home. Hardware: Intel i9, 32 Gb; Roland Integra-7, Presonus 192 & Faderport 8, Royer 121, Adam Sub8 & Neumann 120 monitors.